Well, xp rewards from quests are sounding to be a non-issue in a game where the devs have said the standard xp/level system will not be present.
I've given a bit of thought as to how SE might enable progression through the story.
(Incoming TL;DR...you've been warned ;D)
Personally, I'd be disappointed with a system where you slot weapons with stuff that allows you to learn new abilities/spells and/or exist as the sole means of augmenting your stats. It's been done before in other FF games and is sort of the antithesis of what I've understood SE as saying. With that kind of system, your character isn't developing by how you choose to play it, you're choosing how to develop your character and then playing it based on your choices.
My favorite example of an SE game where you truly develop your character based on how you choose to play it is The Last Remnant, and anyone who has played that game knows that not only did it have the most freeform character development style of any SE RPG to date, it was also the least polished, linear, and ultimately disappointing title SE has put out in a long, long time. From horrendous graphic glitches on the Xbox (the platform TLR was initially released on) to noticeable graphics glitches on the PC and code so poorly optimized that my graphics card would hit 103-104 degrees before it forced a hard system reboot, TLR was ultimately so far below what SE is capable of that I can't help but think it was developed as a "test" of the character development concept for FFXIV.
In terms of the "on-use" development, TLR was awesome. Put that same system into an MMO and I think it would be enormously successful. The one crushing drawback to that system was how your overall development was gauged. TLR assigned your entire group (squad) a "Battle Rank" (BR) that started at 1, and increased as you fought monsters in very much the way you might expect a standard xp/level system to work. The difficulty was that it in no way represented the strength of your squad. You could play the game through to BR50 with one squad, start a new game, and get another squad to BR50 that was easily twice as powerful as the group in your first game.
The reason was because your character development was based on what you did in combat and how often you did it, whereas your BR was based in large part on how many fiends you had killed. If you ran around roflstomping groups of easier monsters, your BR would go up fairly quickly but because you were killing each monster so quickly/easily, you weren't getting a lot of use out of your skills. Compare that to the inverse...fighting small groups of very strong monsters where it takes a relatively long time to kill each one, meaning that your kill count (and thus your BR) stays low, but you're using your abilities a lot more often for each monster, so your characters develop faster.
Obviously, the BR system would not be something you could employ in an MMO, not only because it would be worthless for gauging the level of development for you or a potential party member, but because it's irreversible and discouraged grinding on lower level mobs (ie. no fast farming of lowbie zones for basic materials to craft with/sell).
Then a thought occurred to me that a system to gauge your progress in line with a freeform system already exists in FFXI: the nation rank system. As you progress through your nation's story, your rank increases. Take that concept, merge it with a level-sync style skill cap for content (so people can't get carried through by super-powered friends/guildies without the multiple gear set shenanigans we saw in CoP), and then throw in a skill cap system similar to an FFXI level cap (ie. limit break) and you could have a real winner.
I know that's pretty vague, but allow me to expand on it. You start out with your new character with easy access to the basic job archetype skillsets and head out to do a little entry-level solo grinding. Instead of having all skill categories capped at (your_level * 5) like they are in FFXI, they're capped at 50. Grind for a bit, skill up in your favorite categories, and when you get at least one skill to 25 (for example), a quest opens up the progresses the main story arc. Complete this quest (possibly requiring a group) and your skill cap is increased to 75 and you advance to rank 2. Go out and grind a bit more and once you get at least one skill category to 50, another quest opens up. Complete that and your skill cap is increased to 100 and you advance to rank 3. What this means is that for grouping, if someone says that they are rank three, you know they are the FFXI equivalent of a level 15-20 character in terms of their most developed skill categories.
There would be plenty of room for other quest lines branching from the main story arc. They could be side stories for the sake of side stories, side stories for the sake of unlocking new job archetypes (similar to advanced job quests).
I'm a little bit leary about basically suggesting at a system that involves the equivalent of ongoing limit break quests, but there are two aspects to that which I think would make the idea more appealing. The first is that FFXIV is being put forward as a story-driven MMO. If you don't want to take part in the story, a story-driven MMO is maybe not for you. The second is that there was nothing wrong with the concept of a limit break quest to raise your level cap in FFXI...I just took issue with the implementation (ie. epic grinds to account for abysmal drop rates).
The whole idea isn't fully fleshed out...I have ideas on how to account for people who might want to group to develop new archetypes despite what their "main" rank might be, but it's late. Maybe tomorrow ;D